3rd quadrant. The four 90 degree quadrants together formed 360 degrees. When a given angle is greater than 360 degrees, subtract 360 from it till a value smaller than 360 is obtained. In this way, we can determine the quadrant in which the given angle lies. Here the final angle obtained is 211 degrees (1291-3x360=211).
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Two angles are complementary if they both add up to 90 degrees. This means that a complementary angle would have to be negative 23 degrees if the given angle is 113 (-23+113=90) . However I suspect that you are looking for the supplementary angle. Supplementary angles total 180 degrees. If so, the supplement would be 77 degrees.
If you are really talking about a closed triangle ABC, then the length of side "a" (given as 19) does not matter in the calculation. Sum of the angles of a triangle is 180 degrees. Angle B and C add up to 15 + 65 = 80 degrees. Hence angle A is (180 - 80) = 100 degrees
This is a classic Pythagorean triangle. Although you have given the side lengths, you have NOT given a letter to correspond , with the given side. However, Let 12 be the adjacentr side (base) Let '5' be the opposite side ( perpendicular ) Let '13' by the hypotenuse. Sin(Angle) = opposite / hypotenuse = 5/13 Angle = Sin^(-1) 5/13 = 22.619... degrees. NB This is the angle between the hypotenuse and the base(adjacent) Now 'swopping' things around , we take the angle between the hypotenuse and the perpendicular (opposite) . This now becomes perpendicular(adjacent) and the base becomes the opposite. Hence Sin(angle) = 12/13 Angle = Sin^(-1) 12/13 = 67.380.... degrees. The angle at the 'top' of the triangle. Verification. ' 90 + 67.380... + 22.619... = 180 ( allow for calculator decimals).
Assuming that neither of the given sides is the hypotenuse, then if A is one of the acute angles, tan(A) = 19/63 So A = arctan(19/63) = 16.8 degrees. The other acute angle is 73.2 deg.
that purely depends on the given polygon and any information about it